The art is replete with devices for applying a strip of adhesive along the surface of a member as the member moves along a path relative to the device. Such devices, however, have been found unsuitable for applying adhesive along the side of an elongate member of the type made of fibrous paper like material and used as a core for a roll of paper, primarily because of the somewhat irregular rough peripheral surface defined by fibrous material thin outer layers of which can easily delaminate from the core to form and even rougher and irregular outer surface of the elongate member, and the inability of the pressure rollers or shoes on known adhesive application devices to bring the adhesive into sufficiently intimate engagement with such a peripheral surface to reliably adhere the adhesive to it.